Mohar focused in his study on the \(\alpha \) -Hermitian adjacency matrix where \(\alpha \)  is the primitive sixth root of unity [1]}. While in an earlier study Guo and Mohar considered \(\alpha \)  to be the complex number \(i\)  and demonstrated many interesting spectral properties of the adjacency matrix \(H_i\)  [2]}. Abudayah et al. considered \(\alpha \)  to be the primitive third root of unity \(\gamma \)  instead of the primitive sixth root of unity [3]}. In fact, since \(\gamma ^2=\overline{\gamma }\)  they discovered many interesting spectral properties of \(H_\gamma \) .
